Dear colleagues and researchers,
The Journal of the Korean Society for Industrial and Applied Mathematics (J-KSIAM) Volume 25 Number 3 (September 2021 issue) has been posed on https://www.ksiam.org/archive or other information on the journal is available on the KSIAM website http://www.ksiam.org or https://www.ksiam.org/journal.
The journal is one of Korea Citation Indexed (KCI) journals since 2007 and is indexed in Emerging Sources Citation Index (ESCI) since 2017.
Readers interested in the following articles may download each of articles free of charge from our website and authors are encouraged to submit a paper via the online submission site.
Hi Jun Choe, Editor-in-Chief
Zhiming Chen, Hyeong-Ohk Bae, Tao Tang, Associate Editors-In-Chief
Min Seok Choi, Jae Hoon Jung, Gun Jin Yun, Managing Editors
Review and Implementation of Staggered DG Methods on Polygonal Meshes
Dohyun Kim, Lina Zhao, and Eun-Jae Park
In this paper, we review the lowest order staggered discontinuous Galerkin methods on polygonal meshes in 2D. The proposed method offers many desirable features including easy implementation, geometrical flexibility, robustness with respect to mesh distortion and low degrees of freedom. Discrete function spaces for locally $H^1$ and $H(\tdiv)$ spaces are considered. We introduce special properties of a sub-mesh from a given star-shaped polygonal mesh which can be utilized in the construction of discrete spaces and implementation of the staggered discontinuous Galerkin method. For demonstration purposes, we consider the lowest case for the Poisson equation. We emphasize its efficient computational implementation using only geometrical properties of the underlying mesh.
Fast Pricing of Four Asset Equity-linked Securities Using Brownian Bridge
Changwoo Yoo, Yongho Choi, Sangkwon Kim, Soobin Kwak, Youngjin Hwang, and Junseok Kim
In this study, we present a fast option pricing method for four asset equity-linked securities (ELS) using Brownian bridge. The proposed method is based on Monte Carlo simulation (MCS) and a Brownian bridge approach. Currently, three asset ELS is the most popular ELS among multi-asset ELSs. However, four asset ELS emerged as an alternative to three asset ELS under low interest rate environment to give higher coupon rate to investors. We describe in detail the computational solution algorithm for the four underlying asset step-down ELS. The numerical tests confirm the accuracy and speed of the method.
An Efficient Hybrid Numerical Method for The Two-Asset Black-Scholes PDE
R. Delpasand and M. M. Hosseini
In this paper, an efficient hybrid numerical method for solving two-asset option pricing problem is presented based on the Crank-Nicolson and the radial basis function methods. For this purpose, the two-asset Black-Scholes partial differential equation is considered. Also, the convergence of the proposed method are proved and implementation of the proposed hybrid method is specifically studied on Exchange and Call on maximum Rainbow options. In addition, this method is compared to the explicit finite difference method as the benchmark and the results show that the proposed method can achieve a noticeably higher accuracy than the benchmark method at a similar computational time. Furthermore, the stability of the proposed hybrid method is numerically proved by considering the effect of the time step size to the computational accuracy in solving these problems.
Understanding Non-Negative Matrix Factorization in the Framework of Bregman Divergence
We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.
Fractional Order Thermoelastic Problem for Finite Piezoelectric Rod Subjected to Different Types of Thermal Loading - Direct Approach
Kishor R. Gaikwad, and Vidhya. G. Bhandwalkar
The problem of generalized thermoelasticity of two-temperature for finite piezoelectric rod will be modified by applying three different types of heating applications namely, thermal shock, ramp-type heating and harmonically vary heating. The solutions will be derived with direct approach by the application of Laplace transform and the Caputo-Fabrizio fractional order derivative. The inverse Laplace transforms are numerically evaluated with the help of a method formulated on Fourier series expansion. The results obtained for the conductive temperature, the dynamical temperature, the displacement, the stress and the strain distributions have represented graphically using MATLAB.
Conformable Fractional Sense of Foam Drainage Equation and Construction of Its Solutions
Mohammad T. Darvishi, Mohammad Najafi, and Byeong-Chun Shin
The modified $F$-expansion method is used to construct analytical solutions of the foam drainage equation with time- and space-fractional derivatives. Theconformable derivatives are considered as spacial and temporal ones. As a result, some analytical exact solutions including kink, bright-dark soliton, periodic and rational solutions are obtained.